Question

(a) If r^2 = pq, show that p:q is the duplicate
ratio of (p + r): (q + r).​

Answer 1

Step-by-step explanation:

p:q=(p+r):(q+r)

pq+pr=pq+qr

p=q

r^2=pq

r=p or r=q

r=p=q

Answer 2

Step-by-step explanation:

duplicate ratio of (p+r) : (q+r)

= (p+r)² : (q+r)²

= p²+r²+2pr : q²+r²+2qr

= p²+r²+2pr

q²+r²+2qr

putting the value of r²

= p²+pq+2pr

q²+pq+2qr

= p(p+q+2r)

q(q+p+2r)

=p/q

hence, p:q is the duplicate ratio of (p+q) : (q+r).

say, thank you.